Classical parametric models rely on strong assumptions about the time-to-event distribution. Such strong assumptions allow these models to estimate the underlying stochastic process based on the observed relationship between covariates and time-to-event. However, the predicted probability distribution of these models is over-simplified and often unrealistic. CPH is an example of a parametric statistical model that simplifies the underlying distribution by assuming that the proportional hazard increases constantly over time. The model estimates the hazard function, \(\lambda (t|\textbf {x})\) , the probability that an individual will experience an event within the time \(t\) , given all \(\textbf {x}\)  features (covariates). Although several works such as [1]}, [2]}, [3]} have tried to address the shortcomings of the CPH model to some degree, the over-simplification of the underlying stochastic process limits the flexibility, generalizability, and the prediction power of the CPH model. Besides, the CPH model cannot process longitudinal measurements.
Deep Survival Machines (DSM) [4]} is an example of a machine learning-based parametric model that assumes a combination of multiple Weibull and Log-Normal primitive distributions for the survival function. A deep MLP model is trained to estimate the parameters of those distributions and a scaling factor to determine the weight of each distribution in the overall estimated hazard PDF. Training DSM is rather difficult, as the optimizer is easily diverged when trying to minimize its loss function and the model becomes overfit. Despite delivering a high Concordance Index (CI) score, the model performs poorly when estimating the hitting time of events. The CI score is a metric used for evaluating the ranking performance of survival models. The model is also unable to process longitudinal measurements.
